Denominator: Least Common Denominator & Examples

Denominator are an important part of fractions. Fractions are the numbers that constitute a part of the whole. When an object or collection of objects is divided into equal parts, then each individual part is fraction. A fraction is written as 1/3 or 5/7 or 8/25 etc. Further, fractions are divided into numerator or denominator where the denominator is the total number of equal parts into which the whole is divided. Also, denominator is the number that is placed below the horizontal line of a fraction. It is this bottom number which represents total number of equal parts. Whereas, the numerator is the number of equal parts that are taken out. As is, 3/8, where ‘3’ is the numerator and ‘8’ is the denominator. 

Key Takeaways: Denominator, Numerator, Common Denominator, least common denominator, Rationalise, Fraction, types of fractions

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What is Denominator?

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Denominator can be explained as the number or integer that is placed below the horizontal line of fraction. The denominator is the divisor of the fraction. Also, a denominator can never be equal to zero, otherwise it will result in an indefinite value.

• A denominator is the part of a fraction that comes below the bar of fraction.

• The total number of parts that make up a whole shows the denominator.

• A fraction on the other hand can be expressed as the horizontal line between the two numbers and sometimes represented as ‘/’ as in a/b. This bar is called as fractional bar.

• The number above the fractional bar is called as numerator and one below the fractional bar is called denominator.

• The term denominator is widely taken into account for the concept of ratio and proportion.

• Mathematically, fractions show the division of two number consisting of two parts as numerator and denominator.

• It is not mandatory that only numerical or integer values are expressed in the numerator or denominator form, even variables can be expressed in the same form such as, a/b, p/q, m/n and so on.

Read More: Multiplication and Division of Integers

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Examples of denominator

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As discussed above the denominator is the bottom part of a fraction and here are few examples for it.

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Denominator V/S Numerator

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The differences between numerator and denominator are:

Here two equal parts make up as a whole.

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Common Denominator

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Common denominator can be termed as two or more fractions that have the similar value in the denominator. These are also known to be like and unlike fractions based solely on the similarity between the denominators. 

This can be easily explained while evaluating arithmetic operations such as addition or subtraction, if the fraction has common or same denominator, then it becomes easy to add or subtract them.

Further, the fractions can be divided and multiplied even if the denominators of the fractions are not similar or common.

• Like fractions: 

Like fractions are those fractions with similar denominator.

\(\frac{2}{5}\)+ \(\frac{3}{5}\) = \(\frac{2+3}{5}\) = \(\frac{5}{5}\) = 1.

\(\frac{28}{4}\)+ \(\frac{36}{4}\)= \(\frac{(28 + 36)}{4}\) = \(\frac{64}{4}\) = 16.

• Unlike fractions:

Unlike fractions are those in which we have to convert the fractions first into equal denominator and then further simplify.

\(\frac{1}{2}\)+ \(\frac{1}{4}\) => take LCM of (2,4) = 4.

• \(\frac{1*2}{2*2}\)+ \(\frac{1 * 1}{4 * 1}\) = \(\frac{2}{4}\)+ \(\frac{1}{4}\) = \(\frac{(2+1)}{4}\) = \(\frac{3}{4}\) .

Read More: Real Numbers

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Least Common Denominator

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The least common denominator or LCD of two or more non-zero denominators is defined as the smallest whole number that is divisible by each of the denominators in the given fraction.

Let’s understand the least common denominator by an example with the following steps:

e.g.: subtract 4/3 – 5/2

Step 1) If the given fractions are unlike fractions, then we will find LCM of the denominators ‘2’ and ‘3’. Here LCM (2,3) = 6.

Step 2) Now multiply the first fraction 4/3 with ‘2’ both up and down and this will result in equivalent fraction 8/6. Consequently, multiply the second fraction 5/2 with ‘3’ both up and down and this will result in equivalent fraction 15/6.

Step 3) This step will convert both the fractions to like fractions, which is 8/6 and 15/6.

Step 4) Now the denominators are equal, we can subtract the numerators while denominator remains constant.

\(\frac{8}{6}\)-  \(\frac{15}{6}\) = \(\frac{(8-15)}{6}\) = \(\frac{-7}{6}\).

Also Read: Natural Numbers and Whole Numbers

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Rationalising the Denominator

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To rationalise a denominator means moving the radical term which is square root or a cube root to the numerator, such that the denominator remains as a whole number. When denominator is rationalised, it becomes easy to find the sum or a difference of any fractions.

In much simple term, a fraction whose denominator is a surd can be simplified by making the denominator rational. This process is called a rationalisation of denominator.

If the denominator consists just one term as surd, the denominator can be rationalised by multiplying both numerator as well as denominator by that surd.

Let’s understand with example of rationalising the denominator, \(\frac{\sqrt{2}}{\sqrt{3}}\)

• \(\frac{\sqrt{2} * \sqrt{3}}{\sqrt{3} * \sqrt{3}}\)=  \(\frac{\sqrt{6}}{(\sqrt{3})^2 }\)=  \(\frac{\sqrt{6}}{3 }\) . -------( √3 x √3) = 3.

Also Read: Natural Numbers and Whole Numbers

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Things to Remember

• A denominator must be an integer and it should never be zero because zero never makes up a whole number.

• The term denominator is widely used in the concept of division, fractions, ratio and proportion, and so on.

• Fact: The grip sizes of the tennis racquets are often in the mixed form of numbers. One size is \(3\frac{7}{8}\) inches and other is \(4\frac{3}{8}\) inches.

• The word numerator is derived from Latin verb ‘enumerate’ and the word denominator is derived from same Latin word ‘nomen’ which means ‘name’.

• The word denominator is also termed as ‘divisor’.

• Surds are defined as the expression which includes square root, cube root or another root.

• The term fraction was first coined by Flemish mathematician, military engineer, and Physicist ‘Simon Stevin’.

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